Webrelaunch 2020

Seminar (Completely Integrable Systems II) (Wintersemester 2021/22)

If you are interested in participating in this seminar, please write an email, with possibly interested topics and with the preferred starting date of the seminar, to xian.liao@kit.edu as soon as possible.

This seminar is expected to take place at earliest in November 2021.

Termine
Seminar: Freitag 14:00-15:30 20.30 -1.009
Lehrende
Seminarleitung JProf. Dr. Xian Liao
Sprechstunde: nach Vereinbarung
Zimmer 3.027 Kollegiengebäude Mathematik (20.30)
Email: xian.liao@kit.edu

This seminar is a continuation of the seminar ( Completely Integrable System I) held online in SS2021 at KIT. We propose to continue with Arnold’s well-known book 1 on the mathematical methods on classical mechanics.
We will begin with a review talk on the materials covered in SS2021
0. Newtonian mechanics and Lagrangian mechanics (Sections 1-21 1)
and propose the following topics:
1. Linearization and small oscillations. (Sections 22-23 1)
2. Characteristic frequencies and parametric resonance. (Sections 24-25 1)
3. Inertial forces and Coriolis force. (Sections 26-27 1)
4. Rigid bodies. (Sections 28-29 1)
5. Lagrange’s top. (Sections 30-31 1)
6. Exterior forms and differential forms. (Sections 32-34 1)
7. Exterior differentiation. (Sections 35-36 1)
8. Symplectic structure and Lie algebra. (Sections 37-40 1)
9. Symplectic geometry. (Sections 41-43 1)
10. Integral invariant of Poincaré-Cartan. (Sections 44-45 1)
11. Huygens’ principle. (Section 46 1)
12. Hamilton’s equations. (Sections 47-48 1)
13. Action-angle variables. (Sections 49-50 1)
14. Averaging. (Sections 51-52 1)

Reference:
1. V.I. Arnold, Mathematical Methods of Classical Mechanics. Second Edition. Springer. 1989.

Prerequisites: Analysis I-III, Linear Algebra.
Remarks: We recommend the English presentations, but German is also possible if all other participants agree.